Can you put Multiple physics simulations in one scene simultaneously?
In your physics settings, go to the cache tab and choose free all bakes

Once you have done that choose Bake all dynamics. That should do what you need.

FYI: If you want your smoke simulations to interact, the easiest method is to have them in one simulation, else it becomes tricky. Someone else may have a way to do so but this is the best method I can think of.

Good luck with your project and I hope I helped,

BFB